A Bijection for Eulerian-equivalence Classes of Totally Cyclic Orientations
نویسندگان
چکیده
Gioan showed that the number of cycle reversing classes of totally cyclic orientations of a given graph can be calculated as an evaluation of the corresponding Tutte polynomial. We note that the concept of cycle reversing classes of orientations coincides with that of Eulerianequivalence classes considered by Chen and Stanley, and Kochol. Based on this coincidence, we give a bijective proof of Gioan’s result. Precisely, the main result of the paper is an algorithmic bijection between the set of Eulerian-equivalence classes of totally cyclic orientations and the set of spanning trees without internally active edges.
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عنوان ژورنال:
- Graphs and Combinatorics
دوره 24 شماره
صفحات -
تاریخ انتشار 2008